Lie symmetries and exact solutions of shallow water equations with variable bottom

DOI10.1515/ijnsns-2015-0093zbMath1401.35275OpenAlexW2561896207MaRDI QIDQ1660847

Manoj Pandey

Publication date: 16 August 2018

Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ijnsns-2015-0093

zbMATH Keywords

shallow water equationsLie symmetriesdiscontinuity wave

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

Related Items (7)

Lie symmetry analysis and similarity solutions for the Camassa-Choi equations ⋮ Evolution of contact and weak discontinuity waves in two phase drift flux model ⋮ Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations ⋮ Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates ⋮ Multi-dimensional optimal system and conservation laws for Chaplygin gas Cargo-LeRoux model ⋮ One-dimensional optimal system and similarity transformations for the \(3+1\) Kudryashov-Sinelshchikov equation ⋮ Lie symmetries, one-dimensional optimal system and group invariant solutions for the Ripa system

Cites Work

• Unnamed Item
• Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas
• Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength
• Evolution of weak discontinuities in shallow water equations
• Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas
• Similarity methods for differential equations
• Some exact solutions of nonlinear shallow water equations
• Symmetry analysis of a system of modified shallow-water equations
• Interaction of a weak discontinuity with elementary waves of Riemann problem
• The shallow water equations: explicit solutions and superposition principle
• Symmetry analysis and exact solutions of magnetogasdynamic equations
• Quasilinear Hyperbolic Systems, Compressible Flows, and Waves
• Some exact solutions to the nonlinear shallow-water wave equations
• Group theoretic method for analyzing interaction of a weak discontinuity wave with a bore in shallow water waves
• When nonautonomous equations are equivalent to autonomopus ones
• Symmetries and differential equations

This page was built for publication: Lie symmetries and exact solutions of shallow water equations with variable bottom